Struct fraction::BigInt

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pub struct BigInt { /* private fields */ }

Expand description

A big signed integer type.

Implementations§

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impl BigInt

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Creates and initializes a BigInt.

The bytes are in big-endian byte order.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"A"),
           BigInt::parse_bytes(b"65", 10).unwrap());
assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AA"),
           BigInt::parse_bytes(b"16705", 10).unwrap());
assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"AB"),
           BigInt::parse_bytes(b"16706", 10).unwrap());
assert_eq!(BigInt::from_bytes_be(Sign::Plus, b"Hello world!"),
           BigInt::parse_bytes(b"22405534230753963835153736737", 10).unwrap());

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pub fn from_bytes_le(sign: Sign, bytes: &[u8]) -> BigInt

Creates and initializes a BigInt.

The bytes are in little-endian byte order.

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pub fn from_signed_bytes_be(digits: &[u8]) -> BigInt

Creates and initializes a BigInt from an array of bytes in two’s complement binary representation.

The digits are in big-endian base 2⁸.

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pub fn from_signed_bytes_le(digits: &[u8]) -> BigInt

Creates and initializes a BigInt from an array of bytes in two’s complement.

The digits are in little-endian base 2⁸.

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pub fn parse_bytes(buf: &[u8], radix: u32) -> Option<BigInt>

Creates and initializes a BigInt.

§Examples

use num_bigint::{BigInt, ToBigInt};

assert_eq!(BigInt::parse_bytes(b"1234", 10), ToBigInt::to_bigint(&1234));
assert_eq!(BigInt::parse_bytes(b"ABCD", 16), ToBigInt::to_bigint(&0xABCD));
assert_eq!(BigInt::parse_bytes(b"G", 16), None);

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pub fn from_radix_be(sign: Sign, buf: &[u8], radix: u32) -> Option<BigInt>

Creates and initializes a BigInt. Each u8 of the input slice is interpreted as one digit of the number and must therefore be less than radix.

The bytes are in big-endian byte order. radix must be in the range 2...256.

§Examples

use num_bigint::{BigInt, Sign};

let inbase190 = vec![15, 33, 125, 12, 14];
let a = BigInt::from_radix_be(Sign::Minus, &inbase190, 190).unwrap();
assert_eq!(a.to_radix_be(190), (Sign:: Minus, inbase190));

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pub fn from_radix_le(sign: Sign, buf: &[u8], radix: u32) -> Option<BigInt>

Creates and initializes a BigInt. Each u8 of the input slice is interpreted as one digit of the number and must therefore be less than radix.

The bytes are in little-endian byte order. radix must be in the range 2...256.

§Examples

use num_bigint::{BigInt, Sign};

let inbase190 = vec![14, 12, 125, 33, 15];
let a = BigInt::from_radix_be(Sign::Minus, &inbase190, 190).unwrap();
assert_eq!(a.to_radix_be(190), (Sign::Minus, inbase190));

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pub fn to_bytes_be(&self) -> (Sign, Vec<u8>)

Returns the sign and the byte representation of the BigInt in big-endian byte order.

§Examples

use num_bigint::{ToBigInt, Sign};

let i = -1125.to_bigint().unwrap();
assert_eq!(i.to_bytes_be(), (Sign::Minus, vec![4, 101]));

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pub fn to_bytes_le(&self) -> (Sign, Vec<u8>)

Returns the sign and the byte representation of the BigInt in little-endian byte order.

§Examples

use num_bigint::{ToBigInt, Sign};

let i = -1125.to_bigint().unwrap();
assert_eq!(i.to_bytes_le(), (Sign::Minus, vec![101, 4]));

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pub fn to_u32_digits(&self) -> (Sign, Vec<u32>)

Returns the sign and the u32 digits representation of the BigInt ordered least significant digit first.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from(-1125).to_u32_digits(), (Sign::Minus, vec![1125]));
assert_eq!(BigInt::from(4294967295u32).to_u32_digits(), (Sign::Plus, vec![4294967295]));
assert_eq!(BigInt::from(4294967296u64).to_u32_digits(), (Sign::Plus, vec![0, 1]));
assert_eq!(BigInt::from(-112500000000i64).to_u32_digits(), (Sign::Minus, vec![830850304, 26]));
assert_eq!(BigInt::from(112500000000i64).to_u32_digits(), (Sign::Plus, vec![830850304, 26]));

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pub fn to_u64_digits(&self) -> (Sign, Vec<u64>)

Returns the sign and the u64 digits representation of the BigInt ordered least significant digit first.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from(-1125).to_u64_digits(), (Sign::Minus, vec![1125]));
assert_eq!(BigInt::from(4294967295u32).to_u64_digits(), (Sign::Plus, vec![4294967295]));
assert_eq!(BigInt::from(4294967296u64).to_u64_digits(), (Sign::Plus, vec![4294967296]));
assert_eq!(BigInt::from(-112500000000i64).to_u64_digits(), (Sign::Minus, vec![112500000000]));
assert_eq!(BigInt::from(112500000000i64).to_u64_digits(), (Sign::Plus, vec![112500000000]));
assert_eq!(BigInt::from(1u128 << 64).to_u64_digits(), (Sign::Plus, vec![0, 1]));

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pub fn iter_u32_digits(&self) -> U32Digits<'_>

Returns an iterator of u32 digits representation of the BigInt ordered least significant digit first.

§Examples

use num_bigint::BigInt;

assert_eq!(BigInt::from(-1125).iter_u32_digits().collect::<Vec<u32>>(), vec![1125]);
assert_eq!(BigInt::from(4294967295u32).iter_u32_digits().collect::<Vec<u32>>(), vec![4294967295]);
assert_eq!(BigInt::from(4294967296u64).iter_u32_digits().collect::<Vec<u32>>(), vec![0, 1]);
assert_eq!(BigInt::from(-112500000000i64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);
assert_eq!(BigInt::from(112500000000i64).iter_u32_digits().collect::<Vec<u32>>(), vec![830850304, 26]);

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pub fn iter_u64_digits(&self) -> U64Digits<'_>

Returns an iterator of u64 digits representation of the BigInt ordered least significant digit first.

§Examples

use num_bigint::BigInt;

assert_eq!(BigInt::from(-1125).iter_u64_digits().collect::<Vec<u64>>(), vec![1125u64]);
assert_eq!(BigInt::from(4294967295u32).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967295u64]);
assert_eq!(BigInt::from(4294967296u64).iter_u64_digits().collect::<Vec<u64>>(), vec![4294967296u64]);
assert_eq!(BigInt::from(-112500000000i64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000u64]);
assert_eq!(BigInt::from(112500000000i64).iter_u64_digits().collect::<Vec<u64>>(), vec![112500000000u64]);
assert_eq!(BigInt::from(1u128 << 64).iter_u64_digits().collect::<Vec<u64>>(), vec![0, 1]);

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pub fn to_signed_bytes_be(&self) -> Vec<u8>

Returns the two’s-complement byte representation of the BigInt in big-endian byte order.

§Examples

use num_bigint::ToBigInt;

let i = -1125.to_bigint().unwrap();
assert_eq!(i.to_signed_bytes_be(), vec![251, 155]);

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pub fn to_signed_bytes_le(&self) -> Vec<u8>

Returns the two’s-complement byte representation of the BigInt in little-endian byte order.

§Examples

use num_bigint::ToBigInt;

let i = -1125.to_bigint().unwrap();
assert_eq!(i.to_signed_bytes_le(), vec![155, 251]);

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pub fn to_str_radix(&self, radix: u32) -> String

Returns the integer formatted as a string in the given radix. radix must be in the range 2...36.

§Examples

use num_bigint::BigInt;

let i = BigInt::parse_bytes(b"ff", 16).unwrap();
assert_eq!(i.to_str_radix(16), "ff");

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pub fn to_radix_be(&self, radix: u32) -> (Sign, Vec<u8>)

Returns the integer in the requested base in big-endian digit order. The output is not given in a human readable alphabet but as a zero based u8 number. radix must be in the range 2...256.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from(-0xFFFFi64).to_radix_be(159),
           (Sign::Minus, vec![2, 94, 27]));
// 0xFFFF = 65535 = 2*(159^2) + 94*159 + 27

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pub fn to_radix_le(&self, radix: u32) -> (Sign, Vec<u8>)

Returns the integer in the requested base in little-endian digit order. The output is not given in a human readable alphabet but as a zero based u8 number. radix must be in the range 2...256.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from(-0xFFFFi64).to_radix_le(159),
           (Sign::Minus, vec![27, 94, 2]));
// 0xFFFF = 65535 = 27 + 94*159 + 2*(159^2)

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pub fn sign(&self) -> Sign

Returns the sign of the BigInt as a Sign.

§Examples

use num_bigint::{BigInt, Sign};

assert_eq!(BigInt::from(1234).sign(), Sign::Plus);
assert_eq!(BigInt::from(-4321).sign(), Sign::Minus);
assert_eq!(BigInt::ZERO.sign(), Sign::NoSign);

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pub fn magnitude(&self) -> &BigUint

Returns the magnitude of the BigInt as a BigUint.

§Examples

use num_bigint::{BigInt, BigUint};
use num_traits::Zero;

assert_eq!(BigInt::from(1234).magnitude(), &BigUint::from(1234u32));
assert_eq!(BigInt::from(-4321).magnitude(), &BigUint::from(4321u32));
assert!(BigInt::ZERO.magnitude().is_zero());

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pub fn into_parts(self) -> (Sign, BigUint)

Convert this BigInt into its Sign and BigUint magnitude, the reverse of BigInt::from_biguint().

§Examples

use num_bigint::{BigInt, BigUint, Sign};

assert_eq!(BigInt::from(1234).into_parts(), (Sign::Plus, BigUint::from(1234u32)));
assert_eq!(BigInt::from(-4321).into_parts(), (Sign::Minus, BigUint::from(4321u32)));
assert_eq!(BigInt::ZERO.into_parts(), (Sign::NoSign, BigUint::ZERO));

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pub fn bits(&self) -> u64

Determines the fewest bits necessary to express the BigInt, not including the sign.

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pub fn to_biguint(&self) -> Option<BigUint>

Converts this BigInt into a BigUint, if it’s not negative.

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pub fn pow(&self, exponent: u32) -> BigInt

Returns self ^ exponent.

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pub fn modpow(&self, exponent: &BigInt, modulus: &BigInt) -> BigInt

Returns (self ^ exponent) mod modulus

Note that this rounds like mod_floor, not like the % operator, which makes a difference when given a negative self or modulus. The result will be in the interval [0, modulus) for modulus > 0, or in the interval (modulus, 0] for modulus < 0

Panics if the exponent is negative or the modulus is zero.

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pub fn modinv(&self, modulus: &BigInt) -> Option<BigInt>

Returns the modular multiplicative inverse if it exists, otherwise None.

This solves for x such that self * x ≡ 1 (mod modulus). Note that this rounds like mod_floor, not like the % operator, which makes a difference when given a negative self or modulus. The solution will be in the interval [0, modulus) for modulus > 0, or in the interval (modulus, 0] for modulus < 0, and it exists if and only if gcd(self, modulus) == 1.

use num_bigint::BigInt;
use num_integer::Integer;
use num_traits::{One, Zero};

let m = BigInt::from(383);

// Trivial cases
assert_eq!(BigInt::zero().modinv(&m), None);
assert_eq!(BigInt::one().modinv(&m), Some(BigInt::one()));
let neg1 = &m - 1u32;
assert_eq!(neg1.modinv(&m), Some(neg1));

// Positive self and modulus
let a = BigInt::from(271);
let x = a.modinv(&m).unwrap();
assert_eq!(x, BigInt::from(106));
assert_eq!(x.modinv(&m).unwrap(), a);
assert_eq!((&a * x).mod_floor(&m), BigInt::one());

// Negative self and positive modulus
let b = -&a;
let x = b.modinv(&m).unwrap();
assert_eq!(x, BigInt::from(277));
assert_eq!((&b * x).mod_floor(&m), BigInt::one());

// Positive self and negative modulus
let n = -&m;
let x = a.modinv(&n).unwrap();
assert_eq!(x, BigInt::from(-277));
assert_eq!((&a * x).mod_floor(&n), &n + 1);

// Negative self and modulus
let x = b.modinv(&n).unwrap();
assert_eq!(x, BigInt::from(-106));
assert_eq!((&b * x).mod_floor(&n), &n + 1);

Note that setting/clearing a bit (for positive/negative numbers, respectively) greater than the current bit length, a reallocation may be needed to store the new digits